How do you solve: $lim_(n->oo)(ln(1+e^(2n)))/(ln(1+e^(3n)))$ ? Thanks!

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Answer 1 · 2017-03-18T20:38:48

$2/3$

$(ln(1+e^(2n)))/(ln(1+e^(3n)))=log(e^(2n)(1+e^(-2n)))/log(e^(3n)(1+e^(-3n)))=(log(e^(2n))+log(1+e^(-2n)))/(log(e^(3n))+log(1+e^(-3n)))$

so

$lim_(n->oo)(ln(1+e^(2n)))/(ln(1+e^(3n)))=lim_(n->oo)(2n+log(1+e^(-2n)))/(3n+log(1+e^(-3n))) = 2/3$

How do you solve: lim_(n->oo)(ln(1+e^(2n)))/(ln(1+e^(3n)))lim_(n->oo)(ln(1+e^(2n)))/(ln(1+e^(3n))) ? Thanks!